Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.7% → 97.7%

Time: 5.7s

Alternatives: 10

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Python

def code(x, y, z, t):
	return x + ((y - x) * (z / t))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Python

def code(x, y, z, t):
	return x + ((y - x) * (z / t))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Python

def code(x, y, z, t):
	return x + ((y - x) * (z / t))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]

2. Final simplification 97.6%

   \[\leadsto x + \left(y - x\right) \cdot \frac{z}{t} \]

Alternative 2: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) t))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -5e+153)
     (/ (* y z) t)
     (if (<= (/ z t) -5e+80)
       t_1
       (if (<= (/ z t) -1000000000.0)
         t_2
         (if (<= (/ z t) 5e-26) x (if (<= (/ z t) 5e+159) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+153) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -5e+80) {
		tmp = t_1;
	} else if ((z / t) <= -1000000000.0) {
		tmp = t_2;
	} else if ((z / t) <= 5e-26) {
		tmp = x;
	} else if ((z / t) <= 5e+159) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (-z / t)
    t_2 = y * (z / t)
    if ((z / t) <= (-5d+153)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-5d+80)) then
        tmp = t_1
    else if ((z / t) <= (-1000000000.0d0)) then
        tmp = t_2
    else if ((z / t) <= 5d-26) then
        tmp = x
    else if ((z / t) <= 5d+159) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+153) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -5e+80) {
		tmp = t_1;
	} else if ((z / t) <= -1000000000.0) {
		tmp = t_2;
	} else if ((z / t) <= 5e-26) {
		tmp = x;
	} else if ((z / t) <= 5e+159) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / t)
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+153:
		tmp = (y * z) / t
	elif (z / t) <= -5e+80:
		tmp = t_1
	elif (z / t) <= -1000000000.0:
		tmp = t_2
	elif (z / t) <= 5e-26:
		tmp = x
	elif (z / t) <= 5e+159:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / t))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+153)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -5e+80)
		tmp = t_1;
	elseif (Float64(z / t) <= -1000000000.0)
		tmp = t_2;
	elseif (Float64(z / t) <= 5e-26)
		tmp = x;
	elseif (Float64(z / t) <= 5e+159)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+153)
		tmp = (y * z) / t;
	elseif ((z / t) <= -5e+80)
		tmp = t_1;
	elseif ((z / t) <= -1000000000.0)
		tmp = t_2;
	elseif ((z / t) <= 5e-26)
		tmp = x;
	elseif ((z / t) <= 5e+159)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+153], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+80], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 5e-26], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+159], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -5.00000000000000018e153

   1. Initial program 95.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 93.1%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 95.5%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 95.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 95.5%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around inf 76.6%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]

   if -5.00000000000000018e153 < (/.f64 z t) < -4.99999999999999961e80 or 5.00000000000000003e159 < (/.f64 z t)

   1. Initial program 93.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 93.2%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 93.2%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 93.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 93.5%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around 0 71.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 71.7%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{t}} \]

      2. *-commutative 71.7%

         \[\leadsto -\frac{\color{blue}{x \cdot z}}{t} \]

      3. associate-*r/ 76.8%

         \[\leadsto -\color{blue}{x \cdot \frac{z}{t}} \]

      4. distribute-rgt-neg-in 76.8%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{z}{t}\right)} \]

      5. distribute-neg-frac 76.8%

         \[\leadsto x \cdot \color{blue}{\frac{-z}{t}} \]

   7. Simplified 76.8%

      \[\leadsto \color{blue}{x \cdot \frac{-z}{t}} \]

   if -4.99999999999999961e80 < (/.f64 z t) < -1e9 or 5.00000000000000019e-26 < (/.f64 z t) < 5.00000000000000003e159

   1. Initial program 99.7%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 78.4%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 80.8%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 90.9%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around inf 46.7%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. /-rgt-identity 46.7%

         \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{1}}}{t} \]

      2. associate-/l/ 46.7%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot 1}} \]

      3. *-commutative 46.7%

         \[\leadsto \frac{\color{blue}{z \cdot y}}{t \cdot 1} \]

      4. times-frac 62.3%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{y}{1}} \]

      5. /-rgt-identity 62.3%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{y} \]

   7. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot y} \]

   if -1e9 < (/.f64 z t) < 5.00000000000000019e-26

   1. Initial program 98.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around 0 79.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 3: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+84}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -5e+153)
     (/ (* y z) t)
     (if (<= (/ z t) -1e+84)
       (/ (* x z) (- t))
       (if (<= (/ z t) -1000000000.0)
         t_1
         (if (<= (/ z t) 5e-26)
           x
           (if (<= (/ z t) 5e+159) t_1 (* x (/ (- z) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+153) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+84) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= -1000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-26) {
		tmp = x;
	} else if ((z / t) <= 5e+159) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-5d+153)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-1d+84)) then
        tmp = (x * z) / -t
    else if ((z / t) <= (-1000000000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 5d-26) then
        tmp = x
    else if ((z / t) <= 5d+159) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+153) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+84) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= -1000000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e-26) {
		tmp = x;
	} else if ((z / t) <= 5e+159) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+153:
		tmp = (y * z) / t
	elif (z / t) <= -1e+84:
		tmp = (x * z) / -t
	elif (z / t) <= -1000000000.0:
		tmp = t_1
	elif (z / t) <= 5e-26:
		tmp = x
	elif (z / t) <= 5e+159:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+153)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -1e+84)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (Float64(z / t) <= -1000000000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-26)
		tmp = x;
	elseif (Float64(z / t) <= 5e+159)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+153)
		tmp = (y * z) / t;
	elseif ((z / t) <= -1e+84)
		tmp = (x * z) / -t;
	elseif ((z / t) <= -1000000000.0)
		tmp = t_1;
	elseif ((z / t) <= 5e-26)
		tmp = x;
	elseif ((z / t) <= 5e+159)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+153], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e+84], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-26], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+159], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -5.00000000000000018e153

   1. Initial program 95.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 93.1%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 95.5%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 95.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 95.5%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around inf 76.6%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]

   if -5.00000000000000018e153 < (/.f64 z t) < -1.00000000000000006e84

   1. Initial program 99.7%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 80.8%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around 0 80.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t}\right)} \cdot z \]
   4. Step-by-step derivation

      1. mul-1-neg 80.8%

         \[\leadsto \color{blue}{\left(-\frac{x}{t}\right)} \cdot z \]

      2. distribute-frac-neg 80.8%

         \[\leadsto \color{blue}{\frac{-x}{t}} \cdot z \]

   5. Simplified 80.8%

      \[\leadsto \color{blue}{\frac{-x}{t}} \cdot z \]
   6. Step-by-step derivation

      1. *-commutative 80.8%

         \[\leadsto \color{blue}{z \cdot \frac{-x}{t}} \]

      2. frac-2neg 80.8%

         \[\leadsto z \cdot \color{blue}{\frac{-\left(-x\right)}{-t}} \]

      3. remove-double-neg 80.8%

         \[\leadsto z \cdot \frac{\color{blue}{x}}{-t} \]

      4. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{z \cdot x}{-t}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{z \cdot x}{-t}} \]

   if -1.00000000000000006e84 < (/.f64 z t) < -1e9 or 5.00000000000000019e-26 < (/.f64 z t) < 5.00000000000000003e159

   1. Initial program 99.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 77.4%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 79.7%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 91.2%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 91.2%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around inf 46.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. /-rgt-identity 46.9%

         \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{1}}}{t} \]

      2. associate-/l/ 46.9%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot 1}} \]

      3. *-commutative 46.9%

         \[\leadsto \frac{\color{blue}{z \cdot y}}{t \cdot 1} \]

      4. times-frac 61.9%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{y}{1}} \]

      5. /-rgt-identity 61.9%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{y} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot y} \]

   if -1e9 < (/.f64 z t) < 5.00000000000000019e-26

   1. Initial program 98.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around 0 79.4%

      \[\leadsto \color{blue}{x} \]

   if 5.00000000000000003e159 < (/.f64 z t)

   1. Initial program 92.3%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 97.3%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 97.3%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 92.3%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around 0 71.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 71.5%

         \[\leadsto \color{blue}{-\frac{z \cdot x}{t}} \]

      2. *-commutative 71.5%

         \[\leadsto -\frac{\color{blue}{x \cdot z}}{t} \]

      3. associate-*r/ 74.8%

         \[\leadsto -\color{blue}{x \cdot \frac{z}{t}} \]

      4. distribute-rgt-neg-in 74.8%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{z}{t}\right)} \]

      5. distribute-neg-frac 74.8%

         \[\leadsto x \cdot \color{blue}{\frac{-z}{t}} \]

   7. Simplified 74.8%

      \[\leadsto \color{blue}{x \cdot \frac{-z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+84}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1000000000.0) (not (<= (/ z t) 5e-26)))
   (* z (/ (- y x) t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000000.0) || !((z / t) <= 5e-26)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1000000000.0d0)) .or. (.not. ((z / t) <= 5d-26))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000000.0) || !((z / t) <= 5e-26)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1000000000.0) or not ((z / t) <= 5e-26):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1000000000.0) || !(Float64(z / t) <= 5e-26))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1000000000.0) || ~(((z / t) <= 5e-26)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-26]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e9 or 5.00000000000000019e-26 < (/.f64 z t)

   1. Initial program 96.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 87.7%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around 0 87.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t} + \frac{y}{t}\right)} \cdot z \]
   4. Step-by-step derivation

      1. mul-1-neg 87.7%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{t}\right)} + \frac{y}{t}\right) \cdot z \]

      2. distribute-frac-neg 87.7%

         \[\leadsto \left(\color{blue}{\frac{-x}{t}} + \frac{y}{t}\right) \cdot z \]

      3. +-commutative 87.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} + \frac{-x}{t}\right)} \cdot z \]

      4. distribute-frac-neg 87.7%

         \[\leadsto \left(\frac{y}{t} + \color{blue}{\left(-\frac{x}{t}\right)}\right) \cdot z \]

      5. sub-neg 87.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right)} \cdot z \]

      6. div-sub 89.4%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   5. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   if -1e9 < (/.f64 z t) < 5.00000000000000019e-26

   1. Initial program 98.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around 0 79.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+56} \lor \neg \left(\frac{z}{t} \leq 10^{+20}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e+56) (not (<= (/ z t) 1e+20)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+56) || !((z / t) <= 1e+20)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d+56)) .or. (.not. ((z / t) <= 1d+20))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+56) || !((z / t) <= 1e+20)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e+56) or not ((z / t) <= 1e+20):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e+56) || !(Float64(z / t) <= 1e+20))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e+56) || ~(((z / t) <= 1e+20)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e+56], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e+20]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -5.00000000000000024e56 or 1e20 < (/.f64 z t)

   1. Initial program 95.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 93.9%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around 0 93.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t} + \frac{y}{t}\right)} \cdot z \]
   4. Step-by-step derivation

      1. mul-1-neg 93.9%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{t}\right)} + \frac{y}{t}\right) \cdot z \]

      2. distribute-frac-neg 93.9%

         \[\leadsto \left(\color{blue}{\frac{-x}{t}} + \frac{y}{t}\right) \cdot z \]

      3. +-commutative 93.9%

         \[\leadsto \color{blue}{\left(\frac{y}{t} + \frac{-x}{t}\right)} \cdot z \]

      4. distribute-frac-neg 93.9%

         \[\leadsto \left(\frac{y}{t} + \color{blue}{\left(-\frac{x}{t}\right)}\right) \cdot z \]

      5. sub-neg 93.9%

         \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right)} \cdot z \]

      6. div-sub 95.7%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   5. Simplified 95.7%

      \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   if -5.00000000000000024e56 < (/.f64 z t) < 1e20

   1. Initial program 98.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in y around inf 86.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   4. Simplified 94.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+56} \lor \neg \left(\frac{z}{t} \leq 10^{+20}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+80}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+20}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e+80)
   (/ (* (- y x) z) t)
   (if (<= (/ z t) 1e+20) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e+80) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 1e+20) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-5d+80)) then
        tmp = ((y - x) * z) / t
    else if ((z / t) <= 1d+20) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e+80) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 1e+20) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e+80:
		tmp = ((y - x) * z) / t
	elif (z / t) <= 1e+20:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e+80)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (Float64(z / t) <= 1e+20)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e+80)
		tmp = ((y - x) * z) / t;
	elseif ((z / t) <= 1e+20)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e+80], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+20], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.99999999999999961e80

   1. Initial program 96.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 90.2%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in t around inf 98.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   if -4.99999999999999961e80 < (/.f64 z t) < 1e20

   1. Initial program 99.0%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in y around inf 85.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 93.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   4. Simplified 93.8%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   if 1e20 < (/.f64 z t)

   1. Initial program 95.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 96.7%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around 0 96.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t} + \frac{y}{t}\right)} \cdot z \]
   4. Step-by-step derivation

      1. mul-1-neg 96.7%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{t}\right)} + \frac{y}{t}\right) \cdot z \]

      2. distribute-frac-neg 96.7%

         \[\leadsto \left(\color{blue}{\frac{-x}{t}} + \frac{y}{t}\right) \cdot z \]

      3. +-commutative 96.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} + \frac{-x}{t}\right)} \cdot z \]

      4. distribute-frac-neg 96.7%

         \[\leadsto \left(\frac{y}{t} + \color{blue}{\left(-\frac{x}{t}\right)}\right) \cdot z \]

      5. sub-neg 96.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right)} \cdot z \]

      6. div-sub 98.3%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+80}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+20}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 7: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+20}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -10000000000.0)
   (/ (- y x) (/ t z))
   (if (<= (/ z t) 1e+20) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -10000000000.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 1e+20) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-10000000000.0d0)) then
        tmp = (y - x) / (t / z)
    else if ((z / t) <= 1d+20) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -10000000000.0) {
		tmp = (y - x) / (t / z);
	} else if ((z / t) <= 1e+20) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -10000000000.0:
		tmp = (y - x) / (t / z)
	elif (z / t) <= 1e+20:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -10000000000.0)
		tmp = Float64(Float64(y - x) / Float64(t / z));
	elseif (Float64(z / t) <= 1e+20)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -10000000000.0)
		tmp = (y - x) / (t / z);
	elseif ((z / t) <= 1e+20)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -10000000000.0], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 1e+20], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e10

   1. Initial program 96.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 87.2%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 89.0%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 96.2%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   if -1e10 < (/.f64 z t) < 1e20

   1. Initial program 98.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in y around inf 89.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 96.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   4. Simplified 96.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   if 1e20 < (/.f64 z t)

   1. Initial program 95.5%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 96.7%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around 0 96.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t} + \frac{y}{t}\right)} \cdot z \]
   4. Step-by-step derivation

      1. mul-1-neg 96.7%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{t}\right)} + \frac{y}{t}\right) \cdot z \]

      2. distribute-frac-neg 96.7%

         \[\leadsto \left(\color{blue}{\frac{-x}{t}} + \frac{y}{t}\right) \cdot z \]

      3. +-commutative 96.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} + \frac{-x}{t}\right)} \cdot z \]

      4. distribute-frac-neg 96.7%

         \[\leadsto \left(\frac{y}{t} + \color{blue}{\left(-\frac{x}{t}\right)}\right) \cdot z \]

      5. sub-neg 96.7%

         \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right)} \cdot z \]

      6. div-sub 98.3%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+20}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 8: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1000000000.0) (not (<= (/ z t) 5e-26))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000000.0) || !((z / t) <= 5e-26)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1000000000.0d0)) .or. (.not. ((z / t) <= 5d-26))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000000000.0) || !((z / t) <= 5e-26)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1000000000.0) or not ((z / t) <= 5e-26):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1000000000.0) || !(Float64(z / t) <= 5e-26))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1000000000.0) || ~(((z / t) <= 5e-26)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-26]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e9 or 5.00000000000000019e-26 < (/.f64 z t)

   1. Initial program 96.4%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 87.7%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-div 89.4%

         \[\leadsto \color{blue}{\frac{y - x}{t}} \cdot z \]

      2. associate-/r/ 93.2%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   4. Applied egg-rr 93.2%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   5. Taylor expanded in y around inf 54.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. /-rgt-identity 54.4%

         \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{1}}}{t} \]

      2. associate-/l/ 54.4%

         \[\leadsto \color{blue}{\frac{y \cdot z}{t \cdot 1}} \]

      3. *-commutative 54.4%

         \[\leadsto \frac{\color{blue}{z \cdot y}}{t \cdot 1} \]

      4. times-frac 60.9%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{y}{1}} \]

      5. /-rgt-identity 60.9%

         \[\leadsto \frac{z}{t} \cdot \color{blue}{y} \]

   7. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot y} \]

   if -1e9 < (/.f64 z t) < 5.00000000000000019e-26

   1. Initial program 98.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around 0 79.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e+48) x (if (<= t 1.35e+27) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+48) {
		tmp = x;
	} else if (t <= 1.35e+27) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.2d+48)) then
        tmp = x
    else if (t <= 1.35d+27) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+48) {
		tmp = x;
	} else if (t <= 1.35e+27) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.2e+48:
		tmp = x
	elif t <= 1.35e+27:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.2e+48)
		tmp = x;
	elseif (t <= 1.35e+27)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.2e+48)
		tmp = x;
	elseif (t <= 1.35e+27)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.2e+48], x, If[LessEqual[t, 1.35e+27], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1999999999999999e48 or 1.3499999999999999e27 < t

   1. Initial program 99.6%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around 0 68.5%

      \[\leadsto \color{blue}{x} \]

   if -2.1999999999999999e48 < t < 1.3499999999999999e27

   1. Initial program 96.1%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]

   2. Taylor expanded in z around inf 73.6%

      \[\leadsto \color{blue}{\left(\frac{y}{t} - \frac{x}{t}\right) \cdot z} \]

   3. Taylor expanded in y around inf 51.2%

      \[\leadsto \color{blue}{\frac{y}{t}} \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 38.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 97.6%

   \[x + \left(y - x\right) \cdot \frac{z}{t} \]

2. Taylor expanded in z around 0 40.4%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 40.4%

   \[\leadsto x \]

Developer target: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

  (+ x (* (- y x) (/ z t))))